34 research outputs found
Ensemble-based multiscale modelling of DNA base pair tautomerism in the absence and presence of external electric fields
Löwdin proposed that the base pair double proton transfer (DPT) tautomers, A*T* and G*C*, may cause mutations during the replication process via mismatches, e.g. the pairing of A* with C, and G* with T. This thesis uses multiscale modelling techniques to study base pair tautomerism in a realistic DNA system. Previous studies typically consist of idealised gas-phase quantum models which often produce conflicting results. The aims of this thesis are to i) reassess the viability of base pair tautomerism as a contributory mechanism towards spontaneous single point mutations in DNA and ii) predict how external electric fields (ranging from strengths of 10⁴ V/m to 10⁹ V/m) influence the thermodynamic stability of the tautomers and the kinetics of the DPT reaction. An ensemble of reaction coordinates and the rate coefficients of tautomerism for each base pair in aqueous DNA is calculated using quantum mechanics/molecular mechanics (QM/MM) methods. Performing an ensemble of calculations accounts for the stochastic aspects of my simulations while allowing for easier identification of systematic errors. The results show that DPT between base pairs has a negligible contribution towards spontaneous mutations in DNA. This is because the tautomer has a maximum half-life in the picosecond range, which is significantly smaller than the milliseconds it takes for DNA to unwind during replication, and statistically, they revert towards their canonical forms via a mostly barrierless process. The application of larger electric fields (10⁹ V/m) parallel to base pair hydrogen bonds is found to increase the lifetime of the tautomers by one order of magnitude at most. In the context of mutations in human beings, the effect of external electric fields on base pair tautomerism is deemed insignificant. The ensemble-based methodology utilised in this study has shown that several different proton transfer reaction pathways, each with varying probabilities, occur within the same base pair. This contribution has provided new insight towards the multiscale modelling of biochemical processes, specifically those involving multiple reaction pathways, such as occur in enzyme catalysis
Focused Proof-search in the Logic of Bunched Implications
The logic of Bunched Implications (BI) freely combines additive and
multiplicative connectives, including implications; however, despite its
well-studied proof theory, proof-search in BI has always been a difficult
problem. The focusing principle is a restriction of the proof-search space that
can capture various goal-directed proof-search procedures. In this paper, we
show that focused proof-search is complete for BI by first reformulating the
traditional bunched sequent calculus using the simpler data-structure of nested
sequents, following with a polarised and focused variant that we show is sound
and complete via a cut-elimination argument. This establishes an operational
semantics for focused proof-search in the logic of Bunched Implications.Comment: 18 pages conten
Negation-as-Failure in the Base-extension Semantics for Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS
Definite Formulae, Negation-as-Failure, and the Base-extension Semantics of Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the paradigm of semantics in which
meaning in logic is based on proof (as opposed to truth). A particular instance
of P-tS for intuitionistic propositional logic (IPL) is its base-extension
semantics (B-eS). This semantics is given by a relation called support,
explaining the meaning of the logical constants, which is parameterized by
systems of rules called bases that provide the semantics of atomic
propositions. In this paper, we interpret bases as collections of definite
formulae and use the operational view of the latter as provided by uniform
proof-search -- the proof-theoretic foundation of logic programming (LP) -- to
establish the completeness of IPL for the B-eS. This perspective allows
negation, a subtle issue in P-tS, to be understood in terms of the
negation-as-failure protocol in LP. Specifically, while the denial of a
proposition is traditionally understood as the assertion of its negation, in
B-eS we may understand the denial of a proposition as the failure to find a
proof of it. In this way, assertion and denial are both prime concepts in P-tS.Comment: submitte
Proof-theoretic Semantics and Tactical Proof
The use of logical systems for problem-solving may be as diverse as in
proving theorems in mathematics or in figuring out how to meet up with a
friend. In either case, the problem solving activity is captured by the search
for an \emph{argument}, broadly conceived as a certificate for a solution to
the problem. Crucially, for such a certificate to be a solution, it has be
\emph{valid}, and what makes it valid is that they are well-constructed
according to a notion of inference for the underlying logical system. We
provide a general framework uniformly describing the use of logic as a
mathematics of reasoning in the above sense. We use proof-theoretic validity in
the Dummett-Prawitz tradition to define validity of arguments, and use the
theory of tactical proof to relate arguments, inference, and search.Comment: submitte
From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on
\emph{proof} (as opposed to truth). There are two major approaches to P-tS:
proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former
is a semantics of arguments, and the latter is a semantics of logical constants
in a logic. This paper demonstrates that the B-eS for intuitionistic
propositional logic (IPL) encapsulates the declarative content of a basic
version of P-tV. Such relationships have been considered before yielding
incompleteness results. This paper diverges from these approaches by accounting
for the constructive, hypothetical setup of P-tV. It explicates how the B-eS
for IPL works
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
Defining Logical Systems via Algebraic Constraints on Proofs
We comprehensively present a program of decomposition of proof systems for
non-classical logics into proof systems for other logics, especially classical
logic, using an algebra of constraints. That is, one recovers a proof system
for a target logic by enriching a proof system for another, typically simpler,
logic with an algebra of constraints that act as correctness conditions on the
latter to capture the former; for example, one may use Boolean algebra to give
constraints in a sequent calculus for classical propositional logic to produce
a sequent calculus for intuitionistic propositional logic. The idea behind such
forms of reduction is to obtain a tool for uniform and modular treatment of
proof theory and provide a bridge between semantics logics and their proof
theory. The article discusses the theoretical background of the project and
provides several illustrations of its work in the field of intuitionistic and
modal logics. The results include the following: a uniform treatment of modular
and cut-free proof systems for a large class of propositional logics; a general
criterion for a novel approach to soundness and completeness of a logic with
respect to a model-theoretic semantics; and a case study deriving a
model-theoretic semantics from a proof-theoretic specification of a logic.Comment: submitte